OK, you convinced me your data is huge. You must have many files/folders/links. I have a file system like this. I have to rsync subfolders to keep it from failing.
If /tgtapp is being used for other things:
You may not have enough free space.
You probably have some mess to clean up from your prior attempts.
If /tgtapp is a new file system just for this purpose, clean it up. This deletes everything so make sure you mean it.
rm -fr /tgtapp/*
I would expect the commands from bakunin and methyl to work.
cd /sfsapp; tar cpf - . | (cd /tgtapp; tar xpvf -)
cd /sfsapp; find . -xdev -print | cpio -pdumv /tgtapp
You didn't mention any errors from the tar/cpio you tried. Did it complete silently?
I put the 'v' (verbose) option on the last commands. For now it's probably worth seeing what it's doing. Shrink down your window to speed up the transfer.
as long as both filesystems are on the same box - mount the filesystems both with nolog and noatime and a simple cp -hpr will do the trick for you probably as good as any of the other commands ... make sure that the VG is a scalable one ...
If you would read your own threads than you would have seen this was suggested earlier - together with a few mount options that would make your copy even faster ... see #24